The discrete-continuous model of the one-dimension vibrating mechatronic system

This work presents the analysis of the flexural vibrating one-dimension mechatronic system – the cantilever beam and the piezoelectric transducer bonded with the beam's surface by means of a connection layer. The external RC circuit is adjoined to the transducer's clamps. Dynamic equations of motion of the considered mechatronic system were written down using discrete – continuous mathematical model, taking into consideration the influence of the connection layer and the external electric circuit. The dynamic flexibility of the mechatronic system was assigned on the basis of the approximate Galerkin's method. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The exact and approximate method in mechanical system's analysis

The main aim of this work is to present results of the mechanical system's analysis based on the exact and approximate Galerkin's methods. The considered system is the flexural vibrating one-dimension bending beam. The exact and approximate method were used to assign the dynamic flexibility of the considered system and results of this work were juxtaposed to verify the approximate method's accuracy. The correction coefficients were introduced into the approximate method to unify results of both methods. The aim of this work was to check accuracy of the approximate method and to verify if this method may be used to mechatronic system's analysis, where it is impossible to use the exact method. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correction of Characteristics of Subsystems of Torsionally Vibrating Complex Mechatronic Systems as an Introduction to Solution of Their Inverse Task

In this paper the analysis of torsionally vibrating subsystem of complex mechanical and mechatronic systems by using the the exact and approximate methods were the main purposes to solve the task of assignment of frequency-modal analysis and characteristics of mechatronic system. The characteristic of the elementary subsystems using the exact and approximate methods has been determined according to accepted frequencies and the correction coefficient. The frequencies were chosen from the spectrum in which the synthesis of complex systems will be conducted. It is very important that the difference of flexibility values in the spectrum was minimal. The coefficient of the correction has been determined according to the flexibility values of chosen points and it is equal to quotient of flexibility calculated using the exact method across the flexibility delivered by using the approximate method. The coefficient of the correction is the zero-dimensional quantity. After determination of the correction coefficient the medium value which has been afterwards considered in correlation of dynamic characteristics has been calculated. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximate Galerkin method applied to an analysis of vibration of continuous mechanical systems

Paper presents fundamental assumptions of the approximate Galerkin method application in order to vibration analysis of continuous mechanical systems with different form of vibration and different boundary conditions. Flexural vibration of beams, longitudinal vibration of rods and torsional vibration of shafts with all possible ways of fixing were considered. Analyzed mechanical systems were treated as subsystems of mechatronic systems with piezoelectric transducers. This work was done as an introduction to the analysis of mechatronic systems with piezoelectric transducers used as actuators or passive vibration dampers [1–3]. It is impossible to use an exact Fourier method in this case. This is the reason why the approximate Galerkin method was chosen and analysis of its exactness was done as a first step of this work. Dynamic flexibilities of considered mechanical systems were calculated twice, using exact and approximate methods. Obtained results were juxtaposed and it was proved that in some cases the approximate method should be corrected while in the other it is precise enough. A correction method was proposed and it was assumed that the approximate method can be used in mechatronic systems analysis. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Measuring and designing flexibility as a generalized service degree

The paper designs and measures flexibility as the availability of a dynamic system in an uncertain environment. After a brief discussion of the literature, flexibility is defined essentially as the service degree of a system's dynamic technology. As a further step, this measure is extended to incorporate a system's planning, forecasting, and implementation ability. To obtain a deeper insight into the complex nature of the measure the design of flexibility is discussed within the framework of hierarchical planning.     

Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation

In this paper, nonlinear dynamics, vibration and stability analysis of piezo-visco medium nanoshell resonator (PVM-NSR) based on functionally graded (FG) cylindrical nanoshell integrated with two piezoelectric layers subjected to visco-pasternak medium, electrostatic and harmonic excitations is investigated. Nonclassical method of the electro-elastic Gurtin–Murdoch surface/interface theory with von-Karman–Donnell's shell model as well as Hamilton's principle, the assumed mode method combined with Lagrange–Euler's are considered. Complex averaging method combined with arc-length continuation is used to achieve a numerical solution for the steady state vibrations of the system. The stability analysis of the steady state response is performed. The parametric studies such as the effects of different boundary conditions, different geometric ratios, structural parameters, electrostatic and harmonic excitation on the nonlinear frequency response and stability analysis are studied. The results indicate that near the natural frequency of the nanoshell, it will lead to resonance and will have large motion amplitude and near the resonant frequency, the nanoshell shows a softening type of nonlinear behavior, and the nanoshell bandwidth increases due to nonlinear factors. In this range, nanoshell has three different ranges of motion, of which two are stable and the other unstable, and so the jump phenomenon and saddle-node bifurcation are visible in the behavior of the system. Also piezoelectric voltage influences on static deformation and resonant frequency but has no significant effect on nonlinear behavior and bandwidth and also system very sensitive to the damping coefficient and due to decrease of nano shell stiffness, natural frequency decreases. And also, increasing or decreasing of some parameters lead to increasing or decreasing the resonance amplitude, resonant frequency, the system's instability, nonlinear behavior and bandwidth.     

A Structural Analysis of Performance Deviations: A Time Series Perspective

A time series modelling approach is suggested to analyze the set of performance deviations which are generated by the institution's control system. The purpose of the time series analysis is to provide decision makers with information regarding the structure underlying the set of performance deviations. This structural analysis is intended to facilitate the selection and implementation of appropriate control actions. The basic control system's elements needed to generate information amenable to a time series analysis are specified. A simple case is presented to illustrate the time series method suggested.     

Algorithm of Exact Methods Obtaining of the Solution and Dynamical Flexibilities of Subsystem of the Mechatronic system

In this paper the application of analysis of transverse vibrating subsystem of mechatronic systems by means of the exact were the main purposes of work to solve the task of assignment of frequency-modal analysis and characteristics of mechatronic system. At first the problem of analysis in the form of the one differential equation of motion of mechanical subsystem or of the set of state equations of considered mechatronic model of object has been formulated and solved. Classic method to solve this problem have been used. The considered transverse vibrating mechanical subsystems of mechatronic system are a continuous beams with constant cross-section, with free ends and/or clamped on one end. A ring transducer, which is the integral part of mechatronic system, extorted by harmonic force or voltage excitation, is assumed to be perfectly bonded to the beam surface. Parameters of the transducer have important influence on values of natural frequencies and on form of characteristics of considered mechatronic system. The poles of dynamical characteristic calculated by mathematical exact method and the Galerkin's method have approximately different or the same values; it is depended on the combination of boundary conditions of elementary beam. The results of the calculations were not only presented in mathematical form but also as a transients of examined dynamical characteristic which are function of frequency of assumed excitation. Practical implications of this work is to present the introduction to synthesis of considered class of mechanical and/or mechatronic beam-systems with a constant changeable cross-section. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel analysis method for damping characteristic of a type of double-beam systems with viscoelastic layer

The double-beam system with a viscoelastic layer is a classical mechanical model for many beam-type composite structures. However, few studies have been able to optimize the structure from the perspective of structural damping characteristics. To fully understand the damping characteristics of the viscoelastic double-beam system, an analysis method based on dynamic stiffness method and Wittrick-Williams algorithm is presented in this paper. Through numerical case studies, five typical parameters of the viscoelastic double-beam system are discussed to investigate their influence on the damping characteristic of the system. Finally, the conclusions are used to parametric analysis for a kind of double-sheathing cable systems. Results show that the damping coefficient of the connection layer have a significant effect on the damping characteristic of the double-sheathing cable system compared with other design parameters. The proposed methods and conclusions obtained in this paper are helpful to design and optimize the structural parameters of engineering structures, thus having certain application and promotional value.     

Transformated Hypergraphs in Synthesis of Vibrating Beam-Systems

In this paper the characteristics of subsystems obtained by the approximate and exact method were compared, because purpose is to answer to the question ­ if the method can be used to nominate the characteristics of mechatronic systems. In this paper frequency-modal analysis have been presented for the mechanical system, that means flexibly vibrating free beam. The model of the beam was presented in the five-vertex hypergraph, which in case of approximate frequency-modal analysis we can imitate in three-vertex hypergraph. Such formulation maybe the introduction to synthesis of flexibly vibration complex beam systems with constant cross-section. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solution of Inverse Task of Mechatronic Systems by Means the Classical and Unclassical Methods of Modelling and Analysis

In this paper the modelling by means of the different category graphs and analysis of vibrating subsystem of mechatronic systems by means of the exact and approximate methods have been presented. That approach was to nominate the relevance or irrelevance between the characteristics obtained by means of the exact method (only for the mechanical subsystem) and the approximate method. Such formulation concerns mostly the relevance of the natural frequencies-poles of the characteristics both mechanical subsystems and mechatronic systems. Approximate solutions requiring all the conditions for vibrating mechanical and/or mechatronic systems have been finding and it may be introduction to synthesis of these systems, modeled by different category graphs. Research limitation is following, that torsional vibrating continuous mechanical subsystem and mechatronic systems are linear type. Presentation the introduction to synthesis of considered class of mechatronic bar-systems with a constant changeable cross-section is practical implications of this work. Originality of such formulation is focused on the use of the different category graphs for modelling and synthesising by different methods represented by graphs of vibrating bars to the synthesis of considered discrete-continuous mechatronic systems. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechatronic Subsystem Studied of Approximate Method Modeled by Hypergraph

The transverse vibrating mechatronic subsystem is considered. Integral parts of this system are: a continuous beam with known boundary conditions and a transducer, extorted by harmonic voltage excitation, to be perfectly bonded to the beam surface. Findings this article are dynamical characteristics of the discussed mechatronic and mechanical system to model them by hypergraphs. Research limitation is that the linear mechanical subsystem and linear electric subsystem of mechatronic system has been considered, however for this kind of systems the approach is sufficient. Practical implications of this researches was that global approach is presented, that means in the domain of frequency spectrum analysis. The methods of analysis and obtained results can be base of design and investigation for this type of mechatronic systems. Originality of this paper is that the mechatronic system created from mechanical and electric subsystems with electromechanical bondage has been considered. This approach is different from those considered so far because is it relies on application approximate methods of analysis of mechatronic subsystem and modeling the one by hypergraph [1-7]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element based nonlinear dynamic response of elastically supported piezoelectric functionally graded beam subjected to moving load in thermal environment with random system properties

The second order statistics in terms of mean and standard deviation (SD) of normalized nonlinear transverse dynamic central deflection (NTDCD) response of un-damped elastically supported functionally graded materials (FGMs) beam with surface-bonded piezoelectric layers under the action of moving load are investigated in this paper. The random system properties such as Young's modulus, Poisson's ratio, density, thermal expansion coefficients, piezoelectric materials, volume fraction exponent and external loading are modeled as uncorrelated random variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics combined with Newton–Raphson technique through Newmark's time integrating scheme using finite element method (FEM). The non-uniform temperature distribution with temperature dependent material properties is taken into consideration for consideration of thermal loading. The one parameter Pasternak elastic foundation with Winkler cubic nonlinearity is considered as an elastic foundation. The stochastic based second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are adopted for the solution of nonlinear dynamic governing equation. The influences of volume fraction exponents, temperature increments, moving loads and velocity, nonlinearity, slenderness ratios, foundation parameters and external loadings with random system properties on the NTDCD are examined. The capability of present stochastic model in predicting the NTDCD statistics are compared by studying their convergence with the existing results those available in the literature.     

On optimizing a one-server system with several types of customers

This paper deals with the determination of an optimal strategy for the service system M/M/l with n types of customers under the possibility of the system's ruin. A method how to construct the optimal strategy is presented. A numerical example explaining the described theory is given.     

Calculation of Flexibility of Vibrating Beam as the Subsystem of Mechatronic System by Means the Exact and Approximate Methods

The main aim of this paper is to investigate the transients of characteristics of vibrating beams obtained by the exact and approximate methods and to answer to the question – if the method can be used to nominate the characteristics of mechatronic systems. The approach was to nominate the relevance or irrelevance between the characteristics obtained by considered methods – especially concerning the relevance of the natural frequencies-poles of characteristics of mechanical part of mechatronic system. The main subject of the research is the continuous vibrating beam. Findings of this approach is fact, that approximate solutions fulfill all conditions for vibrating beams and some conditions only, particularly for vibrating beams as the subsystems of mechatronic systems. Practical implications of this paper is the main point is the analysis and the examination of flexibly vibrating discrete-continuous mechatronic systems which characteristics can be nominated with approximate methods only. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Active control of dynamic behaviors of graded graphene reinforced cylindrical shells with piezoelectric actuator/sensor layers

This work investigates the active vibration control and vibration characteristics of a sandwich thin cylindrical shell whose intermediate layer is made of the graphene reinforced composite that is bonded with integrated piezoelectric actuator and sensor layers at its outer and inner surfaces. The volume fraction of graphene platelets in the intermediate layer varies continuously in the shell's thickness direction, which generates position-dependent effective material properties. The constitutive relations of the graphene reinforced composite and piezoelectric materials are given by taking one-dimensional steady thermal field into account. Considering Donnell's shell theory, a final equation of motion in terms of the generalized radial displacement is derived by using Hamilton's principle and Galerkin method. Shell's natural frequencies are derived considering influences of the thermo-electro-elastic field. Introducing a constant velocity feedback control algorithm, active vibration control of the sandwich cylindrical shell is presented by employing the Runge-Kutta method. The feedback control gain has a pronounced effect on the damping, as well as the inertia of the system. Comparisons between the present results and those in other papers are done to validate the present solutions. Influences of weight fractions, distribution patterns and geometrical sizes of graphene platelets, temperature variations, thicknesses of layers and the feedback control gain on the vibration characteristics and active vibration control behaviors of the novel sandwich cylindrical shell are discussed.     

Spectral analysis of a high-order Hermitian algorithm for structural dynamics

The spectral analysis of an efficient step-by-step direct integration algorithm for the structural dynamic equation is presented. The proposed algorithm is formulated in terms of two Hermitian finite difference operators of fifth-order local truncation error and it is unconditionally stable with no numerical damping presenting a fourth-order truncation error for period dispersion (global error). In addition, although it is in competition with higher-order algorithms presented in the literature, the computational effort is similar to that of the classical second-order Newmark’s method. The numerical application for nonlinear structural dynamic problems is also considered.     

Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces

A study on the buckling and dynamic stability of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces is performed in this research. The static and dynamic governing equations of the nanobeam are established with Galerkin method and under Euler–Bernoulli hypothesis. The buckling, post-buckling and nonlinear dynamic stability character of the nanobeam is presented. The quasi-elastic method, Leibnitz’s rule, Runge–Kutta method and the incremental harmonic balanced method are employed for obtaining the buckling voltage, post-buckling characteristics and the boundaries of the principal instability region of the dynamic system. Effects of the electrostatic load, van der Waals force, creep quantity, inner damping, geometric nonlinearity and other factors on the post-buckling and the principal region of instability are investigated.     

Static and dynamic analysis of smart cylindrical shell

Shell type components and structures are very common in many mechanical and structural systems. In smart structural applications, piezolaminated plates and shells are commonly used. In this paper a finite element formulation is presented to model the static and dynamic response of laminated composite shells containing integrated piezoelectric sensors and actuators subjected to electrical, mechanical and thermal loadings. The formulation is based on the first order shear deformation theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A nine-noded degenerated shell element is implemented for the analysis. The model is validated by comparing with existing results documented in the literature. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The influence of the stacking sequence and position of sensors/actuators on the response of the laminated cylindrical shell is evaluated. Numerical results show that piezoelectric sensors/actuators can be used to control the shape and vibration of laminated composite cylindrical shell.     

A new nonlinear dynamic analysis method of rotor system supported by oil-film journal bearings

The strong nonlinear behavior usually exists in rotor systems supported by oil-film journal bearings. In this paper, the partial derivative method is extended to the second-order approximate extent to predict the nonlinear dynamic stiffness and damping coefficients of finite-long journal bearings. And the nonlinear oil-film forces approximately represented by dynamic coefficients are used to analyze nonlinear dynamic performance of a symmetrical flexible rotor-bearing system via the journal orbit, phase portrait and Poincaré map. The effects of mass eccentricity on dynamic behaviors of rotor system are mainly investigated. Moreover, the computational method of nonlinear dynamic coefficients of infinite-short bearing is presented. The nonlinear oil-film forces model of finite-long bearing is validated by comparing the numerical results with those obtained by an infinite-short bearing-rotor system model. The results show that the representation method of nonlinear oil-film forces by dynamic coefficients has universal applicability and allows one easily to conduct the nonlinear dynamic analysis of rotor systems.